Question

Sendo ???? um ângulo agudo de um triângulo retângulo e cos ???? = 5/13. Calcule sin???? e tan �

Answer 1

${ \sin }^{2}x = 1 - { \cos}^{2}x \\ { \sin}^{2}x = 1 - { (\frac{5}{13}) }^{2} = 1 - \frac{25}{169} \\ { \sin}^{2}x = \frac{144}{25}$

$\sin(x) = \sqrt{ \frac{144}{25} } = \frac{12}{5}$

$\tan(x) = \frac{ \sin(x) }{ \cos(x)} = \frac{ \frac{12}{5} }{ \frac{5}{13}} \\ \tan(x) = \frac{12}{5}. \frac{13}{5} = \frac{156}{25}$